1% test file for the Lie package 2 3% 1. n-dimensional Lie algebras with dimL1=1 4% n=6 5 6array lienstrucin(6,6,6)$ 7 8lienstrucin(1,2,2):=lienstrucin(1,2,6):=lienstrucin(1,5,2):=-1$ 9lienstrucin(1,5,6):=lienstrucin(2,5,3):=lienstrucin(2,5,5):=-1$ 10lienstrucin(1,2,3):=lienstrucin(1,2,5):=lienstrucin(1,5,3):=1$ 11lienstrucin(1,5,5):=lienstrucin(2,5,2):=lienstrucin(2,5,6):=1$ 12 13liendimcom1(6); 14 15% transformation matrix 16 17lientrans; 18 19clear lienstrucin$ 20 21% n=8 22 23array lienstrucin(8,8,8)$ 24 25lienstrucin(1,2,2):=lienstrucin(1,5,2):=lienstrucin(2,4,3):=1$ 26lienstrucin(2,4,5):=lienstrucin(4,5,2):=1$ 27lienstrucin(1,2,3):=lienstrucin(1,2,5):=lienstrucin(1,5,3):=-1$ 28lienstrucin(1,5,5):=lienstrucin(2,4,2):=lienstrucin(4,5,3):=-1$ 29lienstrucin(4,5,5):=-1$ 30lienstrucin(1,2,6):=lienstrucin(1,5,6):=lienstrucin(4,5,6):=5$ 31lienstrucin(2,4,6):=-5$ 32 33liendimcom1(8); 34 35% same with verbose output 36 37on tr_lie$ 38 39liendimcom1(8); 40 41clear lienstrucin$ 42 43off tr_lie$ 44 45% 2. 4-dimensional Lie algebras 46 47% Korteweg-de Vries Equation: u_t+u_{xxx}+uu_x=0 48% symmetry algebra spanned by four vector fields: 49% v_1=d_x, v_2=d_t, v_3=td_x+d_u, v_4=xd_x+3td_t-2ud_u 50 51array liestrin(4,4,4)$ 52 53liestrin(1,4,1):=liestrin(2,3,1):=1$ 54liestrin(2,4,2):=3$ 55liestrin(3,4,3):=-2$ 56 57lieclass(4); 58 59clear liestrin$ 60 61 62% dimL1=3, dimL2=3 63 64array liestrin(4,4,4)$ 65 66liestrin(1,2,1):=-6$liestrin(1,2,3):=-2$liestrin(1,2,4):=6$ 67liestrin(1,3,1):=-1$liestrin(1,3,2):=1$liestrin(1,3,4):=1$ 68liestrin(2,3,1):=-3$liestrin(2,3,4):=2$ 69liestrin(2,4,1):=6$liestrin(2,4,3):=2$liestrin(2,4,4):=-6$ 70liestrin(3,4,1):=1$liestrin(3,4,2):=-1$liestrin(3,4,4):=-1$ 71 72lieclass(4); 73 74% same with verbose output 75 76on tr_lie$ 77 78lieclass(4); 79 80% transformation matrix 81 82liemat; 83 84clear liestrin$ 85 86off tr_lie$ 87 88 89end$ 90 91 92